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arXiv · 1812.01287

Generic slow-roll and non-gaussianity parameters in $f(R)$ theories

Tays Miranda·Celia Escamilla-Rivera·Oliver F. Piattella·Júlio C. Fabris
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Abstract

In this paper we establish \textit{formulae} for the inflationary slow-roll parameters $\epsilon$, $\eta$ and $\zeta$ as functions of the Ricci scalar $R$ for $f(R)$ theories of gravity. As examples, we present the analytic and numerical solutions of $\epsilon$, $\eta$ and $\zeta$ as functions of the number of e-folds $N$ in two important instances: for the Starobinsky model and for a $f(R)$ reconstruction of the $\alpha$-Attractors. The highlight of our proposal is to rewrite the slow-roll parameters in terms of $f(R)$, which allows to find directly $n_{\rm s}$, $r$, $\alpha_{\rm s}$ and $f^{\text{equil}}_{\text{NL}}$ as functions of $R$ itself. We obtain that both models indicate a small contribution to the non-Gaussianity parameters, which are in good agreement with current observational constraints.

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BibTeXRIS

Tays Miranda, Celia Escamilla-Rivera, Oliver F. Piattella, Júlio C. Fabris. 2018-12-04. Generic slow-roll and non-gaussianity parameters in $f(R)$ theories. https://doi.org/10.1088/1475-7516%2F2019%2F05%2F028

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